This invention describes various methods for minimizing torque ripple produced by unbalanced phase currents in a sinusoidally excited motor.
Unbalanced phase currents are due primarily to resistance imbalances in the motor and controller. A review is given in T. Jahns and W. Soong, xe2x80x9cPulsating torque minimization techniques for permanent magnet ac motor drivesxe2x80x94a review,xe2x80x9d IEEE Transactions on Industrial Electronics, vol. 43, no. 2, pp. 321-330, April 1996, incorporated herein by reference, of the established methods of minimizing torque ripple along with a summary of the limitations of the existing techniques. An extensive reference list is provided in T. Jahns and W. Soong, which covers the various types of permanent magnet machines including those with trapezoidal back emf and rotor saliency. Torque ripple and pulsations arise from various sources such as magnetic reluctance effects, airgap mmf harmonics, power electronic nonlinearities and unbalanced three phase parameters. Each of these contributors produce a characteristic frequency of torque ripple. A graphical depiction 10 of torque versus position in mechanical degrees for a typical sinusoidal permanent magnet ac motor (PMAC) is shown in FIG. 1.
Referring to FIG. 2, a graphical representation 12 of the spectrum of the torque of FIG. 1 is shown. It is seen in FIG. 2 that the predominant harmonics are the second, sixth, 12th, 18th, 24th and 48th. The 24th and 48th are associated with errors induced in a power electronic motor drive by sensor errors in the position feedback. These components are reduced as the position sensor resolution is increased. The 12th and 18th are created by magnetic reluctance variations. These components have a frequency determined by the number of slots per pole and the presence of rotor saliency in the motor magnetic design. The sixth harmonic is due primarily to harmonic distortion in the motor flux linkage (or back emf) characteristics and power electronic nonlinearities. The second harmonic is due to unbalanced conditions in the three phase system. The literature in motor drive technology contains several methods of minimizing the torque ripple associated with the various harmonics. A disturbance torque model in G. Ferretti, G. Magnani, and P. Rocco, xe2x80x9cModeling, identification and compensation of pulsating torque in permanent magnet ac motors,xe2x80x9d IEEE Transactions on Industrial Electronics, vol. 45, no. 6, pp. 912-920, December 1998, incorporated herein by reference, is proposed which identifies model parameters for all sources of torque ripple during a start-up test sequence for industrial robot manipulators. This method has the drawbacks of a computationally intensive on-line identification algorithm that is not suitable for many applications. In addition, the results are only valid for incremental quasi-static (zero velocity) position control operations.
The frequency components due to magnetic reluctance effects and flux linkage distortion is addressed in S. Clenet, N. Sadowski, S. Astier, and M. Lajoie-Mazenc, xe2x80x9cCompensation of permanent magnet motors torque ripple by means of current supply waveshapes control determined by finite element method,xe2x80x9d IEEE Transactions on Magnetics, vol. 29, no. 2, pp. 2019-23, March 1993, incorporated herein by reference. This method minimizes torque ripple by injecting compensating phase currents based on a profile derived from a priori finite element studies of the motor magnetic characteristics. This method has the restriction that the motor characteristics do not vary significantly with flux level (i.e., minimal saturation effects) or temperature. An adaptive torque ripple minimization scheme is disclosed in J. Holtz and L. Springob, xe2x80x9cIdentification and compensation of torque ripple in high-precision permanent magnet motor drives,xe2x80x9d IEEE Transactions on Industrial Electronics, vol. 43, no. 2, pp. 309-320, April 1996, incorporated herein by reference. This method uses a phase current compensation method as in Clenet, Sadowski, Astier and Lajoie-Mazenc using an on-line parameter identification routine at start-up as in Ferretti, Magnani and Rocco. A high bandwidth controller is used to inject compensating currents into the motor based on look-up tables created from the on-line identification routine. The disadvantages again include numerically intensive algorithms that may not be allowed during start-up of an electric machine in many applications.
K.-Y. Cho, J.-D. Bae, S.-K. Chung, M.-J. Youn, xe2x80x9cTorque harmonics minimization in permanent magnet synchronous motor with back emf estimation,xe2x80x9d IEE Proceedings in Electric Power Applications, vol. 141, no. 6, 1994, pp. 323-330, incorporated herein by reference, presents a method of compensating for flux linkage (back emf) distortion using a predictive current control scheme. This technique is shown to be a practical and effective method in reducing torque ripple due to flux linkage distortion such as the sixth harmonic shown in FIG. 2. As an alternative to active compensation for flux linkage distortion, R. Carlson, A. Tavares, J. Bastos, and M. Lajoie-Mazenc, xe2x80x9cTorque ripple attenuation in permanent magnet synchronous motors,xe2x80x9d Record of IEEE Industrial Applications Society Annual Meeting, 1989, pp. 57-62, incorporated herein by reference, discusses the theory of designing a PMAC with minimized back emf harmonics.
Typically, the largest source of torque ripple is the sixth harmonic induced by flux linkage distortion. Compensation for this component has been covered extensively and most notably in Cho, Bae, Chung and Youn. High frequency ripple caused by position sensor feedback errors can often be minimized by feedback control techniques applied to velocity and torque signals. The next most significant source of torque ripple is due to imbalances in the three phase system. Compensation of circuit imbalance effects in a PMAC motor is addressed in Ferretti, Magnani and Rocco; however it is treated only as a generic disturbance effect without regard to the theoretical background of this component. The effect of circuit imbalances is difficult to compensate for because the source of most imbalances is from thermal effects and component tolerances including variation over product life. There is an extensive literature in the analysis of unbalanced three phase systems. However, most unbalanced electric motor theory is applied to single phase induction motors where the machine torque production is created by a deliberate circuit imbalance (i.e., a split phase machine).
A method of minimizing the torque ripple produced by unbalanced phase currents in a sinusoidally excited motor is disclosed. The method comprises measuring the position of the motor; sampling the phase currents of the motor generating thereby at least one phase current; synchronizing the at least one phase current of the motor with the position of the motor; determining the imbalance in the magnitudes of the at least one phase current of the motor; generating a set of modulation index terms for reducing the imbalance in the magnitudes of the at least one phase current to ensure acceptable torque ripple characteristics over the operating velocity of the motor; and generating a set of minimized line-to-ground voltage commands.